eLitmus Cryptarithmetic Problem – 8

March 23, 2020

Cryptarithmetic Questions asked in eLitmus 8

How To Solve Quickly PrepInsta

Ques. For the following Cryptarithmetic find the answers to the below questions?

           A  N  D
           B  E  T
     --------------
        N  U  D  A
     D  B  J  D
  D  W  E  U
-------------------
  D  A  A  J  A  A
1.Which of the following set contains only even numbers ?
(a) A, D, E(b) A, N, D(c) N, D, B(d) B, E, T
2.Which of the following set contains odd numbers ?
(a) A, N, D(b)  T, B, N(c) J, T, E(d) D, B, E
3.Value of A ?
(a) 1(b) 2(c) 3(d) 4

It is highly suggested to go through these before solving

  1. Cryptarithmetic Introduction
  2. How to Solve Cryptarithmetic Problems
Row1          A N D
Row2          B E T
Row3    ------------
Row4        N U D A
Row5      D B J D
Row6    D W E U
Row7  -------------
Row8    D A A J A A

Step 1

  • As, D x E= _E

Hence Possible values of D and E are

At this stage you can also collect one more clue i.e. D + D = A

Now firstly take Case-1

  • Case 1- E={6} then D={2, 4, 8}
  • Take E=6 and D=2 Put E=6 and D=2 and rewrite the problem again.
Row1          4 N 2 
Row2          B 6 T
Row3    ------------
Row4        N U 2 A
Row5      2 B J 2 
Row6    2 W 6 U
Row7  -------------
Row8    2 A A J A A

Step 2

  • Clearly A = 4
  • As from 10’s digit 2 + 2 = A
  • No carry possible from previous step

Rewrite the whole problem again –

Row1          4 N 2 
Row2          B 6 T
Row3    ------------
Row4        N U 2 4 
Row5      2 B J 2 
Row6    2 W 6 U
Row7  -------------
Row8    2 4 4 J 4 4

Step 3

  • Clearly T = 7
  • 2 x T = _4
    • Only possible for T = {2,4}
    • 2 is already taken so T = 7

Let us now rewrite the problem again –

Row1          4 N 2 
Row2          B 6 7
Row3    ------------
Row4        N U 2 4 
Row5      2 B J 2 
Row6    2 W 6 U
Row7  -------------
Row8    2 4 4 J 4 4

Step 4

  • Step N + B + 6 = _4
    • The resultant is smaller than individual number
    • ie. 6 + 2 values = _4

This is only possible when it is generating carry of 2 or 1

Carry of 2 is not possible as

  • 6 + N + B = 24
  • Assuming max possible values for N and B i.e. 8 and 9
  • 6 + 9 + 8 gives 23

So carry should be 1 and 6 + N + B = 14

Now, 2 + W + 1(carry) = 4

  • This is only possible when W = 1

Creating a sub problem now –

Row1          4 N 2 
Row2              B
Row3    ------------
Row4        2 1 6 U

Now, 4 x B = 21

  • This is only possible when B = 5 and 1 carry from previous step

Now, rewriting the problem again –

Row1          4 N 2 
Row2          5 6 7
Row3    ------------
Row4        N U 2 4 
Row5      2 5 J 2 
Row6    2 7 6 U
Row7  -------------
Row8    2 4 4 J 4 4

Step 5

Now, U + J + U = J

Note – There is no carry from previous step.

  • This is only possible when U = 0 or 5
  • 5 value is already taken thus, U = 0

Clearly, N + 5 + 6 = _4

  • No carry from previous step
  • N = 3

Thus,

  • N + 5 + 6 + 1 (carry) = 4
  • Thus, N = 3

Rewriting the whole problem –

Row1          4 3 2 
Row2          5 6 7
Row3    ------------
Row4        3 0 2 4 
Row5      2 5 J 2 
Row6    2 7 6 0
Row7  -------------
Row8    2 4 4 J 4 4

Step 5

Row1          4 3 2 
Row2              6
Row3    ------------
Row5        2 5 J 2

Clearly

  • 6 x 2 = 12, thus 1 carry to next step
  • 6 x 3 + 1 carry = 19
  • Thus, J  = 9

Problem is solved

Row1          4 3 2 
Row2          5 6 7
Row3    ------------
Row4        3 0 2 4 
Row5      2 5 9 2 
Row6    2 7 6 0
Row7  -------------
Row8    2 4 4 9 4 4

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